Grillage Overview/Introduction
degrees of freedom:
flex only beam
1
3
4
2
we will divert to smartsketch to develop the structure for application of matrix analysis
y
19
22
11
12 c
Mx, θx
=2
4
Mz, θz
=3
b
15
a
5
26
24
14
13
25
23
21
10
fy, v
=1
x
20
7
27
17
16
18
d
8
z
9
6
looking at elements a and b (in x direction) and c and d (in z direction)
using results from smartsketch
4
13
15
6
13
a
22
24
15
1
3
4
2
1
a
b
structure
3
4
2
b
element
1
notes_39_grillage_overview.mcd
initial topology matrix for a and b would be:
 __ __ __ __ 

 __ __ __ __ 
elements a & b
10
11
14
13
13
14
c
16
17
 __ __ __ __ 

 __ __ __ __ 
3
4
2
3
4
c
d
structure
2
d
element
 __ __ __ __ 

 __ __ __ __ 
elements c & d
1
 __ __ __ __ 

 __ __ __ __ 
the remainder of the analysis follows matrix analysis.
let's do example
convert distributed load to equivalent static
External:
Internal:
q
q*l2/8
5/8 q*l
q*l2/12
q*l2/8
5/8 q*l
3/8 q*l
3/8 q*l
Clamped pinned
q
q*l2/12
q*l/2
q*l/2
q*l2/12
q*l/2
q*l/2
Clamped clamped
2
notes_39_grillage_overview.mcd
1